Sunday, 24 August 2014

The recent killing of journalist James Foley has reignited the debate over paying hostage ransom demands. The US, British and many other governments have a clear policy of not paying ransom demands. Does that policy make sense?

The policy has a clear rationale in game theory. To see why consider the very stylized game below. The game begins with the kidnappers deciding whether or not to kidnap. If they kidnap then the hostage's representatives have to decide whether or not to pay the ransom. The numbers give the payoffs to the hostage takers and the hostage's representatives. If the hostage takers do not kidnap then payoffs are 0. If they kidnap and the ransom is paid 100 is transferred from the hostage's representatives to the hostages. If they kidnap and the ransom is not paid then the hostage takers pay some small cost of 10 while the hostage's representatives pay a big cost of 200.

The payoffs in the game are clearly somewhat arbitrary. This, though, doesn't matter too much - it is the relative ordering of payoffs that matter. Specifically, the hostage's representatives have an incentive to pay the ransom because -100 is better than -200. Predicting this, the hostage takers have an incentive to kidnap because 100 is better than 0. There is a unique sub-game perfect Nash equilibrium of 'kidnap, pay ransom'. This equilibrium looks like bad news.

Fortunately, there is another Nash equilibrium. Suppose the hostage's representatives are expected to not pay the ransom. Then the hostage takers should not kidnap because 0 is better than -10. So, 'don't kidnap, don't pay ransom' is also an equilibrium. In a one shot-game this equilibrium is hard to motivate because the hostage takers should be able to predict that the ransom will be paid. In other words, the threat to not pay the ransom is not credible. If, however, the game is repeated many times then the representatives have an incentive to build up a credible reputation for not paying the ransom.

So governments commitment to not paying any ransom is aimed at making the 'don't kidnap, don't pay ransom' equilibrium a reality. And this is the best possible outcome for everyone, bar the hostage takers. There is, however, a fundamental flaw in this logic: According to the equilibrium there should not be any kidnapping. But James Foley, and many others, are kidnapped. Does that mean the policy is not working?

One thing the story so far neglects is heterogeneity. In the game above the hostage takers would rather not kidnap than kidnap and receive no ransom. This is surely the right ordering for most potential instances of kidnap. Suppose, however, that the hostage takers would rather kidnap and receive no ransom than not kidnap. Then we get a game something like that below. In this game the hostage takers have an incentive to kidnap no matter what. And this is arguably more representative of the threat posed by the Islamic State in Syria and Iraq.

In this second game there is a unique equilibrium of 'kidnap, pay ransom'. The hostage's representatives gain nothing from a threat to not pay the ransom. Does this undermine a government policy of never paying hostage takers? We'll the problem here is that the government would need to pay the ransom in some cases and credibly not commit to paying the ransom in others. That seems way too subtle a policy to be realistic. Such policy would also change the incentives of hostage takers. In particular, they would have an incentive to 'burn bridges' in order to create something like the second game above. And it would also change the incentives of potential hostage victims. In particular, there is the moral hazard problem of individuals taking excessive risk.

That kidnapping remains despite a credible commitment to not pay any ransom demands is not, therefore, evidence that government policy is not working. Things would be a lot, lot worse if governments were to start paying up.

Tuesday, 19 August 2014

Petrol prices are one of the more interesting and accessible examples of demand and supply at work. With prices written in bright luminescent letters by the roadside it is a simple task, while driving along, to appreciate the variety of prices on offer. And an interesting economic problem to try and explain that variation in price.

A recent road trip gave us chance to compare prices in a few European countries. It was pretty obvious that prices were higher in Germany than in Austria or Switzerland and higher in Austria and Switzerland than in Luxembourg. These broad differences primarily reflect differences in tax. What I found interesting, however, was that German prices appeared to be squeezed near the borders with Austria and Luxembourg. Anecdotally, at least, it seemed that prices got lower the closer we got to the border. If true, that would be a very nice example of tax incidence at play.

Tax incidence is a fantastic economic concept. But it is also very poorly understood by the average politician, headline writer, member of the general public, and economics student. Confusion primarily comes from the need to throw common sense out of the window. So, let us look at the example of petrol prices in Germany to illustrate how tax incidence works. What I want to do is compare a petrol station in the interior of Germany, say in Hannover, with one near the border with Luxembourg, say in Trier.

The basic difference between Hannover and Trier will be in the price elasticity of demand. In Trier a driver can relatively easily cross into Luxembourg and buy petrol at a cheap rate. That means the average driver in Trier is going to be more price sensitive than the average driver in Hannover. To be more specific suppose that the price of petrol in Luxembourg is €1 per litre. Then the demand curve at the German border (see the right hand figure below) will be flatter above a price of €1 than the demand curve in the Geman interior (left hand figure). One important thing to clarify here is that the demand curves I have drawn show demand for German petrol. Drivers in Trier need petrol just as much as drivers in Hannover it is just that they also have the option to buy Luxembourg petrol. This option flattens demand for German petrol at the border.

There is no reason to suppose the supply of petrol is any different at the border and so I have drawn the supply curve the same in both cases. Now, what happens if the German government puts a tax of €0.50 per litre of petrol? Common sense would say that this pushes the price of petrol up by €0.50. And that common sense would be wrong!
Look first at the left hand figure. A tax of €0.50 pushes up the supply curve by €0.50. The effect of this, however, is to only push up price from €1 per litre to around €1.38 per litre. Why do prices not rise to €1.50? As prices rise drivers demand less petrol because they choose to, say, drive less or drive more economically. If, therefore, the price were to rise by €0.50 there would be excess supply of petrol. In other words petrol companies would be stocking more petrol than drivers want to buy. This is not a good business strategy. And it provides an incentive for those companies to drop prices. At a price of €1.38 demand equals supply.
Lets looks now at the right hand diagram. Here we see that the €0.50 tax only pushes prices up by around €0.18. Why does the price rise a lot less than in the German interior? As the price rises drivers demand a lot less German petrol because they can hop over the border to Luxembourg. This means that prices have to drop a lot in order for demand to equate with supply. And even with these much lower prices demand for German petrol will be lower at the border than the interior.
The basic lesson of tax incidence is that demand and supply determine what will happen to prices. In turn, they determine who will pay most for any tax. Hence a crucial difference between economic incidence and legal incidence. For instance, in our simple example it is drivers who primarily pay for the tax in the interior but petrol companies that pay at the border. No amount of government meddling is going to do anything about that. Taxes, therefore, are a really blunt weapon to target prices or company profits. Something that policymakers seem often blissfully unaware of!